What garages each charge a fixed amount, plus an hourly rate, to service a car. The garage on Main street charged one customer $153 for a 2 hour service appointment, and it charged a second customer $315 for a 5 hour service appointment. The garage on 2nd Street charges $5 lee per hour than the garages on Main Street and $10 more for the fixed amount. How much would the garage on 2nd Street charges for a 3 hour service appointment?

Options

A. 157
B. 174
C. 181
D. 202

Explanation

To solve the problem, we will follow these steps:

1. **Define Variables**: Let \( F \) be the fixed amount charged by the garage on Main Street, and \( H \) be the hourly rate charged by the garage on Main Street.

2. **Set Up Equations**: From the information given:
- For the first customer (2-hour service):
\[ F + 2H = 153 \quad \text{(Equation 1)} \]
- For the second customer (5-hour service):
\[ F + 5H = 315 \quad \text{(Equation 2)} \]

3. **Subtract Equation 1 from Equation 2**:
\[ (F + 5H) - (F + 2H) = 315 - 153 \]
This simplifies to:
\[ 3H = 162 \]

4. **Solve for \( H \)**:
\[ H = \frac{162}{3} = 54 \]

5. **Substitute \( H \) back into Equation 1 to find \( F \)**:
\[ F + 2(54) = 153 \]
Simplifying gives:
\[ F + 108 = 153 \]
Therefore:
\[ F = 153 - 108 = 45 \]

6. **Determine the charges for the garage on 2nd Street**:
- The hourly rate for the garage on 2nd Street is \( H - 5 = 54 - 5 = 49 \).
- The fixed amount for the garage on 2nd Street is \( F + 10 = 45 + 10 = 55 \).

7. **Calculate the charge for a 3-hour service appointment at the garage on 2nd Street**:
\[ \text{Charge} = \text{Fixed Amount} + (\text{Hourly Rate} \times \text{Hours}) \]
\[ \text{Charge} = 55 + (49 \times 3) \]
\[ = 55 + 147 = 202 \]

Thus, the garage on 2nd Street would charge **$202** for a 3-hour service appointment.